Consider a body of mass 1.0kg at rest at the origin at time t = 0 ....

\overset{\to}{F} = \left(\alphat\right)\overset{^}{i} + \beta\overset{^}{j} \left[att = 0, v = 0, \overset{\to}{r} = \overset{\to}{0}\right]$<br >$\alpha = 1, \beta = 1$<br >$\overset{\to}{F} = t\overset{^}{i} + \overset{^}{j}$<br >$m\dfrac{d\overset{\to}{v}}{dt} = t\overset{^}{i} + \overset{^}{j}$<br >On integrating<br >$m\overset{\to}{v} = \dfrac{{t}^{2}}{2}\overset{^}{i} + t\overset{^}{j}$\left[m = 1kg\right]$
\dfrac{d\overset{\to}{v}}{dt}\dfrac{{t}^{2}}{2}\overset{^}{i} + t\overset{^}{j} \left[\overset{\to}{r} = \overset{\to}{0}att = 0\right]$<br >On integrating<br >$\overset{\to}{r} = \dfrac{{t}^{3}}{6}\overset{^}{i} + \dfrac{{t}^{2}}{2}\overset{^}{j}$<br >$\overset{\to}{τ} = - \dfrac{1}{3}\overset{^}{k}$<br >$\overset{\to}{v} = \dfrac{{t}^{2}}{2}\overset{^}{i} + t\overset{^}{j}$<br >At$t = 1\overset{\to}{v} = \left(\dfrac{1}{2}\overset{^}{i} + \overset{^}{j}\right) = \dfrac{1}{2}\left(\overset{^}{i} + 2\overset{^}{j}\right)m / sec$<br >At$t = 1\overset{\to}{s} = \overset{\to}{{r}_{1}} - \overset{\to}{{r}_{0}}$<br >$= \left[\dfrac{1}{6}\overset{^}{i} + \dfrac{1}{2}\overset{^}{j}\right] - \left[\overset{\to}{0}\right]$<br >$\overset{\to}{s} = \dfrac{1}{6}\overset{^}{i} + \dfrac{1}{2}\overset{^}{j}$<br > \left|\overset{\to}{s}\right| = \sqrt{{\left(\dfrac{1}{6}\right)}^{2} + {\left(\dfrac{1}{2}\right)}^{2}} = \dfrac{\sqrt{10}}{6}m$